Higher-order Sasa–Satsuma equation: Nucci’s reduction and soliton solutions

This paper discusses the existence of a diverse range of novel periodic nonlinear waves in the generalized (3+1)-dimensional Sasa–Satsuma equation. This equation models the transmission of femtosecond light pulses through optical fibers, taking into account third-order dispersion, self-frequency shift, and self-steepening effects in all three spatial dimensions of the system. The article presents newly derived periodic wave solutions expressed in terms of Jacobi elliptic functions and also obtains bright and dark soliton solutions in the long-wave limit of the periodic wave solutions. Moreover, a reduction technique employed to obtain another soliton solution and first integral of the considered model. Additionally, the article highlights the necessary fiber parameters required for the existence of these structures and provides graphical illustrations of selected solutions to demonstrate their physical nature.